Inequality

Mathematical Principles & Theorems

Investigates systems of 2D linear inequalities \(a_i x + b_i y \le c_i\). Each linear inequality defines a closed affine half-space \(\mathcal{H}_i \subset \mathbb{R}^2\). The feasible region \(\mathcal{F} = \bigcap_{i=1}^m \mathcal{H}_i\) is a convex polygon (or unbounded polyhedron) by the Minkowski-Weyl theorem. Bounded regions have vertices determined by intersecting pairs of constraint boundary lines.

Operating Instructions

• Enter system of linear inequalities with coefficients \(a, b, c\) and relation (\(\le, \ge, <, >\)).
• Click Plot to render the shaded half-planes on the coordinate grid.
• Observe the overlapping intersection region highlighting the feasible solution space \(\mathcal{F}\).
• Inspect the computed list of boundary vertex coordinates and boundedness indicators.